# Initial velocity

A- Virtual Laboratory part:
Measuring the Acceleration due to Gravity (g)

Theory:
The acceleration that you are going to determine in this experiment is known as the acceleration of free fall, or the acceleration due to gravity. Its value is often taken as 9.81 m/s2 and given the special gravity acceleration symbol (g).
If an object is dropped from a certain height (y) and falls for a time (t), then its equation of motion can be written as:

Where Vo is the initial velocity which is equal to zero if the object falls from rest, and the previous equation can be rewritten as:

To verify the objective of this part using phet interactive simulation, do the following:
2- From the home page of this link, click on lab, from lab window use the provided controllers to adjust the height (y) and the velocity of the lunched ball, the mass, the objects shape (see the Figure ). Adjust the first height at 14m and the velocity must be at zero (Free Fall). Release the ball and use the time meter (control the time meter and fix it at the final point of the ball) to measure the time needed for the ball to travel 14m in vertical direction. Record your data in table 1.
3- Change the height (y) to 13m, release the ball and measure the time needed to travel 13m in the vertical direction. Record the new values in table 1.
4- Repeat step 3 to fill table 1.

Data Analysis:
1) Complete table 1, Calculate ½ t2.
2) Use Excel software to plot the relationship between ½ t2 and y.
3) From the graph find the acceleration of gravity (g) which is equal to the slope.

y(m)
t(s)

14
13
12
11
10
9
8
7
6
5
4

Table 1

Slope = ?

g exp = ?

Questions:
1) What is a free fall?

2) When we say g = 9.81 m/s2, what does this mean?

3) An object is thrown up from the surface of earth, determine the direction of the acceleration in the following cases:
a) The object is going upward.
b) The object at its maximum height.
c) The object is going downward.

4) Convert the value of g from m/s2 to cm/s2

5) Based on your knowledge, why the gravitational acceleration of the earth is much greater than the gravitational acceleration of the moon?

6) Try to drop a paper and a ball from the same height and answer the following questions:

a) What are the forces acting on the ball and the paper?

b) Which object reached the floor faster?

c) Do both objects fall with the same speed? Why? (Elaborate your answer)

© Nawal Nayfeh, Dep. Of Applied Physics and Astronomy

B- Problem-Solving part:

Problem 1:
You throw a rock up into the air as hard as you can, and it went back again to your hand. It stays in the air a total of 6.0 s.

a. Draw a diagram for the rock as it moves, identifying the positive direction of motion.

b. Identify the velocity of the rock at its maximum height.

c. What was the velocity of the rock when you threw it?

Problem 2:
A train moving on a straight track accelerates from rest at 2 m/s2 for 20s. It then moves at constant speed for 2 min. It then decelerates uniformly to a stop in 10s.
a. Identify the type of motion of the train for the first 20s.
b. Find the displacement of the train for the first 20 s.
c. Identify the type of motion of the train for the next 2 min.
d. Find the displacement of the train for the next 2 min.
e. Identify the type of motion of the train for the last 10 s.
f. Find the displacement of the train for the last 10 s.
g. Find the net displacement (Δ x) of the train.

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